Models and Algorithms of Time-Dependent Scheduling

Abstract

This book is a revised and updated edition of monograph [2]. During the eleven years that elapsed from its publication, time-dependent scheduling significantly developed. This fact is confirmed by the volume of the timedependent scheduling literature, counting today about three hundred and fifty references published mainly in SCI journals. Time-dependent scheduling problems also began to be discussed in monographs devoted to such domains as multi-agent scheduling [1] or scheduling with rate-modifying activities [3]. The new edition differs substantially from the previous one. First, in order to increase the overall readability of the monograph, its organization has been changed: now it is composed of twenty one chapters organized into six parts and an appendix. Second, the book has been enriched by the results published after 2008, which considerably increased the volume of the book. Third, pseudo-code of the discussed algorithms is presented in a more readable layout using begin .. end commands and vertical lines which show the internal structure of the algorithms. Fourth, in order to give the reader a deeper insight into the presented material, a number of new examples have been added. Finally, some misprints and inaccuracies have been corrected. The previous edition of the book focused on computational complexity of time-dependent scheduling problems. In this edition, not forgetting about complexity issues, we concentrate on models of time-dependent job processing times and algorithms for solving scheduling problems with such job processing times. This is reflected in a slightly different title of the present book. The first part of the book consists of three chapters and includes the mathematical background of time-dependent scheduling. The aim of this part is to give the reader an introductory view of the presented topics. Therefore, only fundamental notions and concepts are discussed. In Chap. 1, the mathematical notation, basic definitions and auxiliary results used in this book are given. In Chap. 2, essential concepts related to decision problems and algorithms are recalled. The part is completed by Chap. 3, where the definitions and fundamental results of the theory of N P-completeness are presented.